A three-dimensional element-free framework for coupled mechanical-diffusion induced nonlinear deformation of polymeric gels using the IMLS-Ritz method

An element-free framework is developed for the three-dimensional transient process of coupled mechanical-diffusion induced nonlinear deformation of polymeric gels based on the improved moving least-squares Ritz (IMLS-Ritz) method. The method approximates the displacement and chemical potential fields of the gels using the IMLS approximation. An energy formulation for the system is derived and a set of discrete equations is obtained through the Ritz procedure. As a result, the corresponding formulae of the element-free IMLS-Ritz method for three-dimensional transient analysis of the coupled mechanical and diffusion induced nonlinear deformation in polymeric gel are furnished. The numerical accuracy of the IMLS-Ritz method is demonstrated through analyzing the coupled mechanical-diffusion induced transient nonlinear deformation of cubic, thin film and rod gels.